The Brezis–Nirenberg problem for fractional systems with Hardy potentials
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7856
Abstract: In this work, we study the existence of positive solutions to the following fractional elliptic systems with Hardy‐type singular potentials and coupled by critical homogeneous nonlinearities (−Δ)su−μ1u|x|2s=|u|2s∗−2u+ηα2s∗|u|α−2|v|βu+12Qu(u,v)inΩ,(−Δ)sv−μ2v|x|2s=|v|2s∗−2v+ηβ2s∗|u|α|v|β−2v+12Qv(u,v)inΩ,u,v>0inΩ,u=v=0inℝN\Ω, where (− Δ)s denotes the fractional Laplace operator, Ω⊂ℝN… read more here.
Keywords: brezis nirenberg; systems hardy; problem fractional; fractional systems ... See more keywords
Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian
Sign Up to like & getrecommendations! Published in 2017 at "Fractional Calculus and Applied Analysis"
DOI: 10.1515/fca-2017-0061
Abstract: Abstract In this paper, we consider the following Brézis-Nirenberg problem involving the fractional Laplacian operator: (−Δ)su=λu+|u|2s∗−2uinΩ,u=0on∂Ω,$$\begin{array}{} \displaystyle\left\{\begin{array}{ll} (-\Delta)^s u=\lambda u+|u|^{2_s^{*}-2}u & \textrm{in}\ \, \Omega, \\ u=0 & \textrm{on}\ \, \partial\Omega, \end{array} \right. \end{array} $$ where… read more here.
Keywords: involving fractional; array; problem involving; problem ... See more keywords